Existence and Uniqueness of Mild Solutions for the Damped Burgers Equation in Weighted Sobolev Spaces on the Half Line

摘要

This paper addresses an initial boundary value problem for the damped Burgers equation in weighted Sobolev spaces on half line. First, it introduces two normed spaces and present relations between them, which in turn enables us to analysis the existence and uniqueness of a local mild solution and of a global strong solution in these weighted spaces. The paper also studies the well-posedness of this equation in a semi-infinite interval.